Analytic Criteria for the Mechanical and Thermal Stability of Magnetic Stars with Finite Electrical Conductivity

Abstract

The usual assumption of infinite electrical conductivity has been relaxed in a new analytic treatment of the magnetohydrodynamics of a variable magnetic star in the simple one-zone approximation. For a not too low electrical conductivity, the magnetic pressure changes with the mass density as roughly ρ4/3, and the Joule heating rate goes as roughly ρ. The magnetic effective adiabatic exponent of about 4/3 proves to have only a small influence on the criteria for dynamical, secular, and pulsational stability, but the Joule heating rate directly affects the secular and pulsational stability criteria. Thus, a finite electrical conductivity tends to stabilize a magnetic star secularly and to destabilize it pulsationally. These specific results apply, however, only to purely radial perturbations of the star's upper radiative layers.